**2. Post-peak properties of hard rocks at high σ3: conventional and new understanding**

**Figure 1** illustrates the situation with our current knowledge about rock properties beyond the peak stress at triaxial compression of type σ1 > σ2 = σ3. Such

**61**

with rising σ3.

**Figure 1.**

*intermediate and hard rocks.*

*Dramatic Weakening and Embrittlement of Intact Hard Rocks in the Earth's Crust at Seismic…*

stress conditions are normally used in laboratory experiments to simulate on rock specimens stress conditions typical for the earth's crust at different depths. **Figure 1** shows three sets of stress-displacement curves obtained at different levels of confining stress σ3 for rocks of different hardness. Rock hardness here is characterised by uniaxial compressive strength (UCS) and increases from left to right. The curves demonstrate how rock hardness affects post-peak behaviour at rising σ3. Relatively soft rocks on the left (represented by marble with UCS = 130 MPa [24]) exhibit class I behaviour at all levels of σ3 (indicated by blue dotted lines) and show an increase in post-peak ductility with rising σ3. Rocks of intermediate hardness (represented by quartzite with UCS = 180 MPa) exhibit post-peak embrittlement within a certain range of σ3 which is expressed by transition from class I to class II behaviour (indicated by red dotted lines). At lower and higher σ3, the post-peak ductility increases

*Three sets of stress-strain (displacement) curves illustrating features of post-peak behaviour for soft,* 

The typical behaviour of hard rocks (represented by dolerite with

mainly by volcanic and highly metamorphic rocks with UCS > 250 MPa.

on experimental results obtained for softer rocks.

**Figure 1** demonstrates that the effect of embrittlement within a certain range of high σ3 (different for different rocks) increases with increasing rock hardness. The problem is that all existing ultra-stiff servocontrolled testing machines cannot provide controllable failure for hard rocks at high σ3 corresponding to stress conditions of seismic depth for shallow earthquakes. Due to this limitation in testing capability, post-peak properties of hard rocks at high σ3 are experimentally unexplored. Today, post-peak properties of hard rocks at high σ3 and the failure mechanism operating at these conditions are treated by analogy with conventional understanding based

On the basis of comprehensive analysis of side effects accompanying extreme ruptures, an unknown before shear rupture mechanism and inaccessible post-peak properties of hard rocks generated by this mechanism were recently identified [16–23]. In this section we will demonstrate only the fundamental difference

UCS = 300 MPa) is characterised by dramatic embrittlement at high σ3 leading to extreme class II behaviour. It is important to note that the transition from class I to class II for this rock occurs at σ3 = 30 MPa. At relatively low σ3, the post-peak failure can be controlled both for class I and class II on stiff and servocontrolled testing machines. However, at σ3 > 50 MPa, the failure process associated with propagation of a shear rupture becomes uncontrollable and abnormally violent. With rising σ<sup>3</sup> rock brittleness and the violence increase. However, we can suppose that at very high σ3, by analogy with intermediate rocks, hard rocks should also return to more ductile behaviour. Hard rocks with similar post-peak behaviour are represented

*DOI: http://dx.doi.org/10.5772/intechopen.85413*

*Dramatic Weakening and Embrittlement of Intact Hard Rocks in the Earth's Crust at Seismic… DOI: http://dx.doi.org/10.5772/intechopen.85413*

**Figure 1.**

*Earth Crust*

shallow earthquakes.

stresses activating earthquakes, small stress drop and specific depth-frequency distribution of earthquake hypocentres with a maximum at a special depth [1–9]. The nature of friction and stick-slip instability for rocks in association with earthquakes has been comprehensively studied during the last half of a century [1, 5, 7, 10–15]. At the same time, post-peak properties of intact hard rocks under high confining stresses σ3 corresponding to seismic depths of shallow earthquakes are still unexplored experimentally. The reason for that is uncontrollable and violent failure of rock specimens even on modern stiff and servocontrolled testing machines. Today, post-peak properties of hard rocks at high σ3 and the failure mechanism operating at these conditions are treated by analogy with conventional understanding based on experimental results obtained for softer rocks. The paper shows that this analogy is unacceptable because the real properties of hard rocks at high σ3 differ fundamentally from the conventional understanding. The lack of knowledge about post-peak properties of the majority of the earthquake host rocks prevents us from understanding and quantifying the contribution of these rocks to

The paper discusses a recently identified shear rupture mechanism operating in hard rocks under high σ3 that is responsible for extreme rupture dynamics [16–23]. The mechanism was identified on the basis of comprehensive analysis of side effects accompanying extreme ruptures. The new mechanism provides two remarkable features in the rupture head: (1) low shear resistance approaching zero and (2) highly amplified shear stresses. The combination of these features allows for a shear rupture to propagate through intact rock spontaneously at very low shear stresses applied with the absorption of a small amount of energy which indicates dramatic rock weakening and embrittlement at high σ3. Due to the weakening and embrittlement during the failure process, the stress-strain curves for laboratory specimens look very specific in the post-peak region indicating 'abnormal' properties.

The paper demonstrates that in the earth's crust, the new mechanism is active in the vicinity of pre-existing faults only and can provide the formation of new dynamic faults in intact rocks at very low shear stresses (up to an order of magnitude less than the frictional strength). The fault propagation is accompanied by extremely low rupture energy and small stress drop which can be smaller than for stick-slip instability on pre-existing faults. It is shown that some earthquake features currently attributed to the stick-slip instability on pre-existing faults can be provided by the new mechanism for ruptures propagating in intact rocks. Some of these features are nucleation on the basis of pre-existing faults, recurring instability on a pre-existing fault, activation of earthquakes at low shear stresses, small stress

The unknown before 'abnormal' properties of hard rocks at high σ3 make intact rocks more dangerous in respect of shallow earthquakes than pre-existing faults because the new mechanism can generate dynamic faults at shear stresses significantly below the frictional strength. The proximity of the pre-existing fault to the zone of dynamic new fracture development in intact rock creates the illusion of frictional stick-slip instability on the pre-existing fault, thus concealing the real situation. According to the new knowledge, intact hard rocks adjoining pre-existing

**2. Post-peak properties of hard rocks at high σ3: conventional and new** 

**Figure 1** illustrates the situation with our current knowledge about rock properties beyond the peak stress at triaxial compression of type σ1 > σ2 = σ3. Such

drop and specific depth-frequency distribution of hypocentres.

faults represent the general source of shallow earthquakes.

**60**

**understanding**

*Three sets of stress-strain (displacement) curves illustrating features of post-peak behaviour for soft, intermediate and hard rocks.*

stress conditions are normally used in laboratory experiments to simulate on rock specimens stress conditions typical for the earth's crust at different depths. **Figure 1** shows three sets of stress-displacement curves obtained at different levels of confining stress σ3 for rocks of different hardness. Rock hardness here is characterised by uniaxial compressive strength (UCS) and increases from left to right. The curves demonstrate how rock hardness affects post-peak behaviour at rising σ3. Relatively soft rocks on the left (represented by marble with UCS = 130 MPa [24]) exhibit class I behaviour at all levels of σ3 (indicated by blue dotted lines) and show an increase in post-peak ductility with rising σ3. Rocks of intermediate hardness (represented by quartzite with UCS = 180 MPa) exhibit post-peak embrittlement within a certain range of σ3 which is expressed by transition from class I to class II behaviour (indicated by red dotted lines). At lower and higher σ3, the post-peak ductility increases with rising σ3.

The typical behaviour of hard rocks (represented by dolerite with UCS = 300 MPa) is characterised by dramatic embrittlement at high σ3 leading to extreme class II behaviour. It is important to note that the transition from class I to class II for this rock occurs at σ3 = 30 MPa. At relatively low σ3, the post-peak failure can be controlled both for class I and class II on stiff and servocontrolled testing machines. However, at σ3 > 50 MPa, the failure process associated with propagation of a shear rupture becomes uncontrollable and abnormally violent. With rising σ<sup>3</sup> rock brittleness and the violence increase. However, we can suppose that at very high σ3, by analogy with intermediate rocks, hard rocks should also return to more ductile behaviour. Hard rocks with similar post-peak behaviour are represented mainly by volcanic and highly metamorphic rocks with UCS > 250 MPa.

**Figure 1** demonstrates that the effect of embrittlement within a certain range of high σ3 (different for different rocks) increases with increasing rock hardness. The problem is that all existing ultra-stiff servocontrolled testing machines cannot provide controllable failure for hard rocks at high σ3 corresponding to stress conditions of seismic depth for shallow earthquakes. Due to this limitation in testing capability, post-peak properties of hard rocks at high σ3 are experimentally unexplored. Today, post-peak properties of hard rocks at high σ3 and the failure mechanism operating at these conditions are treated by analogy with conventional understanding based on experimental results obtained for softer rocks.

On the basis of comprehensive analysis of side effects accompanying extreme ruptures, an unknown before shear rupture mechanism and inaccessible post-peak properties of hard rocks generated by this mechanism were recently identified [16–23]. In this section we will demonstrate only the fundamental difference

**Figure 2.** *Some typical features of post-peak behaviour of hard rocks at highly confined compression illustrated by experimental results obtained for dolerite specimens at σ3 = 60 MPa and σ3 = 75 MPa.*

between the conventional and new understanding of post-peak properties of hard rocks at high σ3. The new failure mechanism and more detailed information about hard rock behaviour in laboratory and natural conditions will be discussed in the following sections of the paper.

**Figure 2** demonstrates some features typical for post-peak behaviour of hard rocks at high σ3. It shows experimental results obtained for dolerite specimens with UCS = 300 MPa tested under σ3 = 60 MPa and σ3 = 75 MPa. **Figure 2a** illustrates schematically a cylindrical specimen equipped with an axial gauge and a load cell as used in experiments. The failure process at high σ3 is always associated with a shear rupture propagation shown by a dotted line on the specimen body. **Figure 2b** shows two stress-strain curves where points A indicate the final stage of controllable post-peak failure after which the spontaneous and violent shear rupture propagation took place. **Figure 2c** shows enlarged fragments of the stress-strain curves involving the post-peak stage. The post-peak curves here reflecting real rock properties up to point A were easily obtained in static regime due to controllable reverse deformation of the specimen provided by the servo-controlled system. However, beyond point A, the failure control became impossible. The reason for that is as follows. At point A, the post-peak modulus (represented by a red line on the graphs) became practically equal to the unloading elastic modulus (represented by a blue line on the graphs) which corresponds to the extreme Class II behaviour. The unloading modulus was determined by unloading the specimen tested under σ3 = 75 MPa at the peak stress (marked as n-n on the graph). The fact that the post-peak modulus and unloading modulus are practically coincide indicates that the post-peak rupture energy beyond points

**63**

rupture mechanism.

machine.

**Figure 3.**

*Dramatic Weakening and Embrittlement of Intact Hard Rocks in the Earth's Crust at Seismic…*

A is vanishingly small. The controllable failure at this situation becomes impossible because the existing testing machines unable to provide sufficiently fast the specimen unloading to stop the rupture propagation. The spontaneous failure at high σ3 is usually abnormally violent and accompanied by strong sound and shudder of the testing

*Schematic illustration of the fundamental difference between the conventional and the new understanding of* 

Because during the spontaneous failure the testing machine cannot provide sufficiently fast unloading of the specimen to follow the actual post-peak modulus, the readings of gauges obtained at this stage of failure do not reflect the actual post-peak properties of the failing specimen. At the same time, the conducted above analysis of the post-peak modulus at point A allows supposing that the stress-strain curve beyond point A should be very close (practically coincide) to the unloading elastic curve. Another very important post-peak feature typical for hard rocks at high σ3 can be observed on the stress-time curves recorded by the load cell in **Figure 2d**. These curves demonstrate that during the spontaneous failure the specimen strength at a certain stage becomes significantly below the static frictional strength, the level of which is represented by a horizontal dotted line ∆σf. The static frictional strength was determined experimentally by deforming the failed specimen at low strain rates. The least level of the specimen transient strength during the spontaneous failure corresponding to point B is indicated by a horizontal dotted line ∆σtr that is about 10 times less than the static frictional strength ∆σf. It will be shown later that the observed in these experiments the extreme Class II behaviour and the abnormally low specimen transient strength are provided by the new shear

Using the obtained results, we can formulate a hypothesis about the fundamental difference in post-peak properties of hard rocks at high σ3 in terms of the conventional and the new understanding illustrated in **Figure 3**. **Figure 3a** shows

*DOI: http://dx.doi.org/10.5772/intechopen.85413*

*post-peak properties of hard rocks tested at high σ3.*

*Dramatic Weakening and Embrittlement of Intact Hard Rocks in the Earth's Crust at Seismic… DOI: http://dx.doi.org/10.5772/intechopen.85413*

**Figure 3.**

*Earth Crust*

**62**

following sections of the paper.

**Figure 2.**

between the conventional and new understanding of post-peak properties of hard rocks at high σ3. The new failure mechanism and more detailed information about hard rock behaviour in laboratory and natural conditions will be discussed in the

*Some typical features of post-peak behaviour of hard rocks at highly confined compression illustrated by* 

*experimental results obtained for dolerite specimens at σ3 = 60 MPa and σ3 = 75 MPa.*

**Figure 2** demonstrates some features typical for post-peak behaviour of hard rocks at high σ3. It shows experimental results obtained for dolerite specimens with UCS = 300 MPa tested under σ3 = 60 MPa and σ3 = 75 MPa. **Figure 2a** illustrates schematically a cylindrical specimen equipped with an axial gauge and a load cell as used in experiments. The failure process at high σ3 is always associated with a shear rupture propagation shown by a dotted line on the specimen body. **Figure 2b** shows two stress-strain curves where points A indicate the final stage of controllable post-peak failure after which the spontaneous and violent shear rupture propagation took place. **Figure 2c** shows enlarged fragments of the stress-strain curves involving the post-peak stage. The post-peak curves here reflecting real rock properties up to point A were easily obtained in static regime due to controllable reverse deformation of the specimen provided by the servo-controlled system. However, beyond point A, the failure control became impossible. The reason for that is as follows. At point A, the post-peak modulus (represented by a red line on the graphs) became practically equal to the unloading elastic modulus (represented by a blue line on the graphs) which corresponds to the extreme Class II behaviour. The unloading modulus was determined by unloading the specimen tested under σ3 = 75 MPa at the peak stress (marked as n-n on the graph). The fact that the post-peak modulus and unloading modulus are practically coincide indicates that the post-peak rupture energy beyond points

*Schematic illustration of the fundamental difference between the conventional and the new understanding of post-peak properties of hard rocks tested at high σ3.*

A is vanishingly small. The controllable failure at this situation becomes impossible because the existing testing machines unable to provide sufficiently fast the specimen unloading to stop the rupture propagation. The spontaneous failure at high σ3 is usually abnormally violent and accompanied by strong sound and shudder of the testing machine.

Because during the spontaneous failure the testing machine cannot provide sufficiently fast unloading of the specimen to follow the actual post-peak modulus, the readings of gauges obtained at this stage of failure do not reflect the actual post-peak properties of the failing specimen. At the same time, the conducted above analysis of the post-peak modulus at point A allows supposing that the stress-strain curve beyond point A should be very close (practically coincide) to the unloading elastic curve. Another very important post-peak feature typical for hard rocks at high σ3 can be observed on the stress-time curves recorded by the load cell in **Figure 2d**. These curves demonstrate that during the spontaneous failure the specimen strength at a certain stage becomes significantly below the static frictional strength, the level of which is represented by a horizontal dotted line ∆σf. The static frictional strength was determined experimentally by deforming the failed specimen at low strain rates. The least level of the specimen transient strength during the spontaneous failure corresponding to point B is indicated by a horizontal dotted line ∆σtr that is about 10 times less than the static frictional strength ∆σf. It will be shown later that the observed in these experiments the extreme Class II behaviour and the abnormally low specimen transient strength are provided by the new shear rupture mechanism.

Using the obtained results, we can formulate a hypothesis about the fundamental difference in post-peak properties of hard rocks at high σ3 in terms of the conventional and the new understanding illustrated in **Figure 3**. **Figure 3a** shows six stages of shear rupture propagation through a specimen. The rupture incorporates a process zone ℓp representing the rupture head and a frictional zone ℓf located behind the head. In intact zone ℓs, located in front of the process zone, shear resistance corresponds to the intact material strength τs, while behind the process zone (in zone ℓf), shear resistance is equal to the frictional strength τf. After completion of the process zone at stage 1, the length of ℓp stays constant, while the length of the frictional zone ℓf increases during the rupture propagation.

In accordance with conventional understanding, the specimen strength beyond the peak stress (transient strength τtr) at any failure stage is determined roughly by the sum of shear resistance of all three zones along the propagating rupture (intact, process and frictional):

$$
\pi\_{tr} = \pi\_s \frac{l\_s}{l} + \pi\_p \frac{l\_p}{l} + \pi\_f \frac{l\_f}{l} \tag{1}
$$

Shear resistance of the process zone here can be determined roughly as τp = (τs + τf)/2.

**Figure 3b** illustrates the conventional understanding of post-peak properties of hard rocks at high σ3. Points on the graph indicate six identical failure stages shown for the specimen in **Figure 3a**. The specimen strength at each stage is described by Eq. (1). Here, during the failure process, the transient strength decreases gradually by substituting the material strength with frictional strength. At stages 5 and 6, the specimen strength is determined by friction in the fault which is considered today to be the lower limit on rock shear strength. The post-peak rupture energy between stages 1 and 5 corresponds to the shaded area under the curve.

**Figure 3c** illustrates the new understanding of post-peak properties of hard rocks at high σ3. It will be shown later that the new mechanism provides very low shear resistance of the completed process zone which can be τ<sup>p</sup> ≈ 0.1τf. Furthermore, the new mechanism represents a very powerful stress amplifier (based on an unknown before principle) providing high shear stresses in the process zone at low shear stresses applied. These two unique features after completion of the process zone at stage 1 make it possible for the shear rupture to propagate through intact rock even at very low shear stresses applied τ which can be significantly (up to an order of magnitude) less than the frictional strength. In this case the specimen transient strength at controllable failure is determined solely by the process zone strength: τtr = τp.

**Figure 3c** shows that controllable failure can be provided if the testing machine is capable to unload the specimen up to the level τtr = τp at the moment of completion of the process zone (stage 1). The extreme Class II stage beyond the peak stress is associated with the initial formation of the process zone. After that the rupture can propagate statically through the specimen at applied stresses slightly above τtr = τp which represents the specimen strength between failure stages 1 and 4. The rupture propagation through intact rock at a constant shear stress significantly below the frictional strength we will classify as Class III. The post-peak rupture energy between stages 1 and 4 corresponds to the shaded area on the graph. This very low energy absorption implies very high brittleness of the material at the failure process. After stage 5 when the process zone has crossed the specimen, the situation changes. The specimen strength at stages 5 and 6 is determined by friction in the developed fault. To provide displacement along the developed fault, it is necessary to increase the applied stress up to τf.

It should be noted that if the testing machine cannot provide sufficiently fast unloading at the moment of completion of the process zone (stage 1), the failure process will be spontaneous and violent because in this case the applied stress

**65**

**high σ<sup>3</sup>**

**Figure 4.**

*Dramatic Weakening and Embrittlement of Intact Hard Rocks in the Earth's Crust at Seismic…*

exceeds the material strength which corresponds to τtr = τp. It is important to note also that in the case of spontaneous failure, the load cell adjoining the specimen (see **Figure 3a**) will record the variation of stresses applied to the specimen from the testing machine but not the actual material strength determined by the process zone. The actual strength of the process zone can be reflected by the load cell when the applied stress decreases to the level τtr = τp which corresponds to point B in **Figure 2d**. The new shear rupture mechanism that is responsible for the discussed 'abnormal' post-peak properties including Class III behaviour of hard rocks under

*a) and b) Nature of shear rupture growth in hard rocks at high σ3. c) and d) The difference between the conventional (frictional) and the new (fan-hinged) shear rupture mechanisms. e) Illustration of the fan-*

**3. General principles of the new mechanism operating in hard rocks at** 

**Figure 4** illustrates the nature of shear rupture propagation in brittle intact rocks at high σ3. In **Figure 4a** a shear rupture propagates from left to right under stresses σ1, σ3, σn and τ representing the applied major and minor stresses and the induced normal and shear stresses. Shear ruptures are known to propagate through brittle rocks because of the creation of an echelon of tensile cracks at the rupture tip generated along the major stress that is at angle α<sup>o</sup> ≈ (30° ÷ 40°) to the shear rupture plane [25–28]. The echelon of inclined tensile cracks and inter-crack slabs forms a typical structure of shear ruptures illustrated by a photograph in **Figure 4b** (modified from [29]). Horizontal lines here indicate the rupture faces. It was observed

high σ3 will be introduced in the next sections.

*structure formation and propagation through a rock specimen.*

**3.1 Structure of shear ruptures**

*DOI: http://dx.doi.org/10.5772/intechopen.85413*

*Dramatic Weakening and Embrittlement of Intact Hard Rocks in the Earth's Crust at Seismic… DOI: http://dx.doi.org/10.5772/intechopen.85413*

**Figure 4.**

*Earth Crust*

process and frictional):

process zone strength: τtr = τp.

necessary to increase the applied stress up to τf.

τp = (τs + τf)/2.

τ*tr* = τ*<sup>s</sup>*

six stages of shear rupture propagation through a specimen. The rupture incorporates a process zone ℓp representing the rupture head and a frictional zone ℓf located behind the head. In intact zone ℓs, located in front of the process zone, shear resistance corresponds to the intact material strength τs, while behind the process zone (in zone ℓf), shear resistance is equal to the frictional strength τf. After completion of the process zone at stage 1, the length of ℓp stays constant, while the length of the

In accordance with conventional understanding, the specimen strength beyond the peak stress (transient strength τtr) at any failure stage is determined roughly by the sum of shear resistance of all three zones along the propagating rupture (intact,

**Figure 3b** illustrates the conventional understanding of post-peak properties of hard rocks at high σ3. Points on the graph indicate six identical failure stages shown for the specimen in **Figure 3a**. The specimen strength at each stage is described by Eq. (1). Here, during the failure process, the transient strength decreases gradually by substituting the material strength with frictional strength. At stages 5 and 6, the specimen strength is determined by friction in the fault which is considered today to be the lower limit on rock shear strength. The post-peak rupture energy between

**Figure 3c** illustrates the new understanding of post-peak properties of hard rocks at high σ3. It will be shown later that the new mechanism provides very low shear resistance of the completed process zone which can be τ<sup>p</sup> ≈ 0.1τf. Furthermore, the new mechanism represents a very powerful stress amplifier (based on an unknown before principle) providing high shear stresses in the process zone at low shear stresses applied. These two unique features after completion of the process zone at stage 1 make it possible for the shear rupture to propagate through intact rock even at very low shear stresses applied τ which can be significantly (up to an order of magnitude) less than the frictional strength. In this case the specimen transient strength at controllable failure is determined solely by the

**Figure 3c** shows that controllable failure can be provided if the testing machine is capable to unload the specimen up to the level τtr = τp at the moment of completion of the process zone (stage 1). The extreme Class II stage beyond the peak stress is associated with the initial formation of the process zone. After that the rupture can propagate statically through the specimen at applied stresses slightly above τtr = τp which represents the specimen strength between failure stages 1 and 4. The rupture propagation through intact rock at a constant shear stress significantly below the frictional strength we will classify as Class III. The post-peak rupture energy between stages 1 and 4 corresponds to the shaded area on the graph. This very low energy absorption implies very high brittleness of the material at the failure process. After stage 5 when the process zone has crossed the specimen, the situation changes. The specimen strength at stages 5 and 6 is determined by friction in the developed fault. To provide displacement along the developed fault, it is

It should be noted that if the testing machine cannot provide sufficiently fast unloading at the moment of completion of the process zone (stage 1), the failure process will be spontaneous and violent because in this case the applied stress

*<sup>l</sup>* (1)

*l* \_\_*s <sup>l</sup>* <sup>+</sup> <sup>τ</sup>*<sup>p</sup> lp*\_\_ *<sup>l</sup>* <sup>+</sup> <sup>τ</sup>*<sup>f</sup> lf* \_\_

Shear resistance of the process zone here can be determined roughly as

frictional zone ℓf increases during the rupture propagation.

stages 1 and 5 corresponds to the shaded area under the curve.

**64**

*a) and b) Nature of shear rupture growth in hard rocks at high σ3. c) and d) The difference between the conventional (frictional) and the new (fan-hinged) shear rupture mechanisms. e) Illustration of the fanstructure formation and propagation through a rock specimen.*

exceeds the material strength which corresponds to τtr = τp. It is important to note also that in the case of spontaneous failure, the load cell adjoining the specimen (see **Figure 3a**) will record the variation of stresses applied to the specimen from the testing machine but not the actual material strength determined by the process zone. The actual strength of the process zone can be reflected by the load cell when the applied stress decreases to the level τtr = τp which corresponds to point B in **Figure 2d**. The new shear rupture mechanism that is responsible for the discussed 'abnormal' post-peak properties including Class III behaviour of hard rocks under high σ3 will be introduced in the next sections.
